Publishing is for songwriters/publishing companies.

These days, producers are far more likely to have a hand in writing the music to a song (ie Neptunes) than a producer in the classic sense like Bob Rock, Tommy LiPuma, or your favorite, Quincy Jones.

Producers get paid either through a upfront negotiated flat fee (which is most common these days) or they get production royalties (usually about 3% of the MSRP) or a combination of both depending on what the producer negotiates.

Song: Billie Jean
Songwriter: Michael Jackson
Publsher: Mijac Music adm. by Warner Tamerlane
Producer: Quincy Jones

Any money that Billie Jean earns through licensing (film, TV, etc) or airplay (radio) will be divided btwn MJ and Warner Tamerlane dependent upon the percentage split agreed upon by the two parties. Quincy would not get a cut of that money. If Quincy agreed to a producing royalty, then he will receive money from the actual sales of the song.

If you submit a song to Mrs. Carter and she chooses it for inclusion on her album, you have to agree to share writing and production credit with her, whether she does any work or not.

Case in point: "If I Were A Boy" was written by BC Jean (lyrics and melody) and Toby Gad (music). Toby Gad produced the song. The song had been completed. When Beyonce chose to record the song for her album, she did not alter the lyrics or music. Toby Gad agreed to share production credit with Beyonce. Gad and Jean shared songwriting credit with Beyonce.

Since Gad shopped the song without Jean's knowledge, Jean was unaware of the "Beyonce arrangement" and was upset that Beyonce would get writing credit for a song she did not write and made a stink about it. Of course, Beyonce's team hushed her with a cash settlement.